Abstract: Let $R$ be a $2$-torsion free semiprime ring and $U$ a nonzero square closed Lie ideal of $R$. In this paper it is shown that if $f$ is either an endomorphism or an antihomomorphism of $R$ such that $f(U)=U$, then $f$ is strong commutativity preserving on $U$ if and only if $f$ is centralizing on $U$.